Figure 4. Thermal calibration and sideband cooling of fundamental mechanical mode with red-detuned pumping.

(a) Selected thermo-mechanical noise spectra for different temperatures and n_p=6·10⁴. (b) Plot of the measured mechanical mode temperature of device A, expressed in phonon occupation n_m, as a function of cryostat temperature at V_g=3.002 V where ω_m/2π=53.7 MHz and n_p=6·10⁴. On the right y-axis, we display the variance of the vibration amplitude 〈z²〉, which is obtained by integrating the thermal resonance, as is shown in a. The phonon occupation is quantified with (see Supplementary Note 3). The error bars are given by the standard deviation of 5 spectral measurements. (c) Mechanical displacement spectral density S_z measured for different pump photon number. The cryostat temperature is 15 mK. Note that the curves are not offset. (d) Displacement imprecision as a function of cavity pump photon population. The line is a fit of equation (3) with n_add=32. (e) Average phonon number n_m as a function of n_p. The error bars are given by the standard deviation of five spectral measurements.